基于主成分分析和梯度重构的全波形反演

传统全波形反演追求模拟记录与实际地震记录的完全匹配，在实际地震记录含有噪声时反演结果较差。为此，在分析了随机噪声对全波形反演影响机制的基础上，利用主成分分析和梯度重构的方法对梯度进行优化。首先对由各炮梯度组成的矩阵进行主成分分析，再选取贡献较大的主成分对梯度进行重构。在残差信噪比较高时，梯度重构能够获得准确的梯度，不影响反演的收敛速度；在信噪比较低时，重构的梯度能阻止模型朝着错误的方向更新，为下一频段反演提供合理的初始模型。模型实验表明，采用主成分分析和梯度重构方法的全波形反演具有较强的抗噪能力，在信噪比较低时也能得到正确的反演结果。

Full waveform inversion based on principal component analysis and gradient reconstruction

When applied to heavily noisy data,full waveform inversion (FWI) usually provides a terrible result because conventional FWI concentrates on complete consistency between simulated data and original records.This article analyzes the influence of random noise on FWI and proposes a new gradient processing method based on principal component analysis (PCA) and gradient reconstruction.Firstly we apply PCA to the matrix consisted of every shot gradient,and pick specific principal components with high representativeness.Then we can reconstruct gradient with these principal components.When the signal-to-noise ratio (SNR) of residuals is relatively high,this method can reconstruct accurate gradient which will help the objective function decrease effectively.If the SNR is low,the reconstructed gradient will prevent the inversion process from accessing to a wrong model,which can provide a more reasonable initial model for the next frequency band.Numerical experiments show that FWI based on PCA and gradient reconstruction is more robust than conventional methods,which obtains acceptable results even when the SNR is low.